Finite Group Databasebeta

← #215633

Subgroups — #215633

Order 512.

738 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2666C211yesmaximal, characteristic
2#21916C211yesmaximal, characteristic
3#21916C211yesmaximal, characteristic
4#9883C212yesmaximal
5#9882C212yesmaximal
6#9881C212yesmaximal
7#9881C212yesmaximal
8#8705C212yesmaximal
9#8703C212yesmaximal
10#2666—24no—
11#2666—24no—
12C2×#400C411yescharacteristic
13C2×#400C411yescharacteristic
14C2×#398C411yescharacteristic
15C2×#398C411yescharacteristic
16C2×#398C411yescharacteristic
17C2×#398C411yescharacteristic
18C2×#395C411yescharacteristic
19C2×#395C411yescharacteristic
20C2×#391C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#387C2211yescharacteristic
23C2×#387C2211yescharacteristic
24C2×#383C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27#1917—24no—
28#1917—24no—
29#1817C2212yes—
30#1817C2212yes—
31#1797C2212yes—
32#1797C2212yes—
33#1749C2212yes—
34#1749C2212yes—
35#1280C2214yes—
36#1280C2214yes—
37#1280C2214yes—
38#1280C2214yes—
39C23×Q8C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C4⋊C4C2×C411yescharacteristic
43C22×C4⋊C4C2×C411yescharacteristic
44C22×C4⋊C4C2×C411yescharacteristic
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C4⋊C4C2×C411yescharacteristic
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C42C2311yescharacteristic
54C22×C42C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C2×C4⋊C8—22no—
57C2×C4⋊C8—22no—
58C2×C22⋊C8C2314yes—
59C2×C22⋊C8C2314yes—
60C2×#97—22no—
61C2×#97—22no—
62#400—24no—
63#400—24no—
64#398—24no—
65#398—24no—
66#398—24no—
67#398—24no—
68#395—24no—
69#395—24no—
70#391—22no—
71#391—22no—
72#389—22no—
73#389—22no—
74#387—22no—
75#387—22no—
76#387—22no—
77#387—22no—
78#383—22no—
79#383—22no—
80#382—22no—
81#382—22no—
82C4×C4⋊C4D414yes—
83C4×C4⋊C4D414yes—
84C2×#95C2×C411yescharacteristic
85C2×#95C2×C411yescharacteristic
86C2×#95C2×C411yescharacteristic
87C2×#95C2×C411yescharacteristic
88C2×#95C2×C411yescharacteristic
89C2×#95C2×C411yescharacteristic
90C2×#95C2×C411yescharacteristic
91C2×#95C2×C411yescharacteristic
92C2×#95C2×C411yescharacteristic
93C2×#95C2×C411yescharacteristic
94C2×#95C2×C411yescharacteristic
95C2×#95C2×C411yescharacteristic
96C2×#95C2×C411yescharacteristic
97C2×#95C2×C411yescharacteristic
98C2×#95C2311yescharacteristic
99C2×#95C2311yescharacteristic
100C2×#95C2311yescharacteristic
101C2×#95C2311yescharacteristic
102#336—22no—
103#336—22no—
104#336—24no—
105#336—24no—
106#336—22no—
107#336—22no—
108C22×Q8—22no—
109C22×Q8—42no—
110C22×Q8—81no—
111C22×Q8—81no—
112C23×C4C22×C411yescharacteristic
113C23×C4C22×C411yescharacteristic
114C23×C4C22×C411yescharacteristic
115C23×C4C22×C411yescharacteristic
116C23×C4C22×C411yescharacteristic
117C23×C4C22×C411yescharacteristic
118C23×C4C22×C411yescharacteristic
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C2411yescharacteristic
127C22×C8—24no—
128C22×C8—24no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—42no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—81no—
146C2×C4⋊C4—81no—
147C2×C4⋊C4—81no—
148C2×C4⋊C4—81no—
149C2×C4⋊C4—81no—
150C2×C4⋊C4—81no—
151C2×C4⋊C4—81no—
152C2×C4⋊C4—81no—
153C2×C4⋊C4C22⋊C414yes—
154C2×C4⋊C4C22⋊C414yes—
155C2×C42—24no—
156C2×C42—81no—
157C2×C42—81no—
158C2×C42C2×D412yes—
159C2×C42C2×D412yes—
160C2×C42C2×D412yes—
161C2×C42C2×D412yes—
162C2×C42C2×D412yes—
163C2×C42C2×D412yes—
164C4⋊C8—82no—
165C4⋊C8—82no—
166C22⋊C8—28no—
167C22⋊C8—28no—
168#97—82no—
169#97—82no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182#95—21no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95C22⋊C414yes—
191#95C22⋊C414yes—
192C24C23×C411yescharacteristic
193C2×Q8—44no—
194C2×Q8—82no—
195C2×Q8—82no—
196C2×Q8—88no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C2×C22⋊C412yes—
250C22×C4C2×C22⋊C412yes—
251C22×C4C2×C22⋊C412yes—
252C22×C4C2×C22⋊C412yes—
253C22×C4C2×C22⋊C412yes—
254C22×C4C2×C22⋊C412yes—
255C22×C4C22×D411yescharacteristic
256C22×C4C22×D411yescharacteristic
257C22×C42−1+414yes—
258C2×C8—44no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—44no—
262C2×C8—44no—
263C2×C8—44no—
264C4⋊C4—44no—
265C4⋊C4—44no—
266C4⋊C4—44no—
267C4⋊C4—44no—
268C4⋊C4—44no—
269C4⋊C4—82no—
270C4⋊C4—82no—
271C4⋊C4—82no—
272C4⋊C4—82no—
273C4⋊C4—82no—
274C4⋊C4—82no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C42—24no—
278C42—24no—
279C42—42no—
280C42—42no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C22×C22⋊C411yescharacteristic
288C23#51912yes—
289C23#56812yes—
290C23#56812yes—
291Q8—88no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4#53612yes—
354C2×C4#53612yes—
355C8—84no—
356C8—84no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22#231011yescharacteristic
364C22#287911yescharacteristic
365C22#287911yescharacteristic
366C22#288311yescharacteristic
367C22#288411yescharacteristic
368C22#288811yescharacteristic
369C22#288911yescharacteristic
370C22#298714yes—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—42no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C2—24no—
388C2#1740511yescharacteristic
389C2#1740611yescharacteristic
390C2#1740911yescharacteristic
391C2#1741011yescharacteristic
392C2#2182311yescharacteristic
393C2#2182811yescharacteristic
394C2#2183211yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#26662
#219162
#98832
#98822
#98812
#87052
#87032